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One major reason to mine asteroids and the moon is to get water for rocket fuel in space, rather than having to lift it out of Earth's gravity well.

Suppose that you've got to build a generic solar-powered water-fueled rocket for something like an unmanned space tug. You have to budget tankage, solar collector, engine, and associated structure/modules.

Assuming that you have access to mined water in orbit at each possible destination, what makes more sense: building a solar-thermal water rocket, that simply uses giant mirrors to focus solar radiation, boil water, and eject it out the back of your rocket (low Isp but very simple), or solar panels that convert solar energy to electricity that is used for electrolysis to split water into hydrogen and oxygen to burn in a thruster?

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I would not put solar collectors on a tug. It'd be terribly inefficient. Solar collectors will keep fixed orbits at a location tugs come to visit and refuel at. The solar collector will break water into oxygen and hydrogen. These will either be used by tugs directly as fuel, or be used to synthesize a more convenient fuel.

Alternatively, keep oxygen for the life support, and use hydrogen with NTRs on tugs.

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Eh, CO2 scrubbers are simple enough. If you're going to be going into space you can afford to bring your oxygen with you.

But this leads to a secondary question: if you have a fuel depot with access to water, capable of performing electrolysis, is it more efficient (from an Earth-launch perspective) to provide tugs with hydrogen and oxygen to burn, or with hydrogen to put into an NTR? Or would the simplicity of just giving them water to put into their NTR work as well?